Problem 1. Solve the following initial value problem, Ut = kuza XER, t > 0, XER. ult=0 = g(x) (a) For g(x) = ear? What values of a E R is our solution well defined? (b) For g(x) = {-4 1 - x' x 1. Problem 1. Solve the following initial value problem, Ut = kuza XER, t > 0, XER. ult=0 = g(x) (a) For g(x) = ear? What values of a E R is our solution well defined? (b) For g(x) = {-4 1 - x' x 1